Group action invariants
| Degree $n$ : | $21$ | |
| Transitive number $t$ : | $138$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,16,2,18,3,17)(4,20,5,21,6,19)(7,9)(10,12)(13,15), (1,17,5,7,13,2,16,6,9,14)(3,18,4,8,15)(10,21,12,20,11,19) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 5040: $S_7$ 10080: $S_7\times C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $S_7$
Low degree siblings
42T2539, 42T2540, 42T2541Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 118 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $7348320=2^{5} \cdot 3^{8} \cdot 5 \cdot 7$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |